Operatic heroine's career's beginning to take off (5)
I believe the answer is:
mimic
'take off' is the definition.
(thesaurus)
'operatic heroine's career's beginning' is the wordplay.
'operatic heroine' becomes 'mimi'.
'beginning' suggests taking the first letters.
The first letter of 'careers' is 'c'.
'mimi'+'c'='MIMIC'
'to' is the link.
(Other definitions for mimic that I've seen before include "Person imitating another" , "Imitate, copy appearance or mannerisms" , "Act like" , "Take (someone) off" , "Imitate for humorous reasons" .)